To the left, an 8 × 8
grid can be covered by one square (measuring 8 × 8), by four squares (measuring
4 × 4 each), or by ten squares (one 5 × 5, three 3 × 3,
two 2 × 2, and four 1 × 1).
Find all values of n for which it is impossible to cover an
8 × 8 grid with n squares of
integer side length.
three six-sided dice A, B, and C, with the following numbers on their sides:
A: 2, 2, 4, 4, 9, 9
B: 1, 1, 6, 6, 8, 8
C: 3, 3, 5, 5, 7, 7
is the probability that:
· A produces a higher number than B?
· B produces a higher number than C?
· C produces a higher number than A?
you find another set of face values for A, B, and C that yield the same
properties? (Does such a set even exist?)
A 40‑inch straightedge
(without markings) is divided into four pieces. The length of each piece is an
integer number of inches. These four pieces, when used in tandem, can be used
to measure any integer length from 1 to 40 inches.
What are the lengths of the
The rectangle shown consists of eight squares. The length of each side of each
square is 1 unit. The length of the shortest path from A to C using the lines
shown is 6 units.
many different six-unit paths are there from A to C?